A roller mill of the type to which the invention relates is known from German Auslegeschrift No. 19 38 722. In this roller mill a sifter part is arranged above a grinding part containing a grinding face with roller bodies rolling on it, and the sifting chamber of the sifter part is in flow connection with the grinding part, so that an air stream coming from the grinding part and charged with comminuted material passes through a ring of guide vanes provided on the upper outer periphery of the sifting chamber (as a connecting passage) and into the sifting chamber. The material for grinding which has not yet been sufficiently comminuted (coarse material) is to be separated off in this sifting chamber and returned to the grinding face from the hopper arranged at the bottom. In addition, a fan wheel which rotates about a vertical shaft is arranged in the region above the ring of guide vanes and the sifted air stream charged with fine material and flowing upwards to the exhaust pipe passes axially through this fan wheel so that further sifting of the fine material carried upwards with the air stream can be achieved.